We present a theoretical framework showing that popular LLM alignment methods--including RLHF and its variants--can be understood as divergence estimators between aligned (safe or preferred) and unaligned (harmful or less-preferred) distributions. This perspective explains the emergence of separation in the latent space between safe and harmful prompts after alignment. As an application of our general divergence framework, we propose KLDO, a novel KL divergence-based alignment method, and empirically validate its effectiveness. We further show that using compliance-refusal datasets, rather than standard preference-based datasets, leads to stronger separation and improved safety alignment. Finally, to quantify the separation effect, we propose a distance-based metric in the prompt representation space, which also acts as a statistically significant indicator for model safety.

Diffusion models have achieved impressive performance in generating high-quality and diverse synthetic data. However, their success typically assumes a classbalanced training distribution. In real-world settings, multi-class data often follow a long-tailed distribution, where standard diffusion models struggleproducing lowdiversity and lower-quality samples for tail classes. While this degradation is well-documented, its underlying cause remains poorly understood. In this work, we investigate the behavior of diffusion models trained on long-tailed datasets and identify a key issue: the latent representations (from the bottleneck layer of the U-Net) for tail class subspaces exhibit significant overlap with those of head classes, leading to feature borrowing and poor generation quality. Importantly, we show that this is not merely due to limited data per class, but that the relative class imbalance significantly contributes to this phenomenon. To address this, we propose COntrastive Regularization for Aligning Latents (CORAL), a contrastive latent alignment framework that leverages supervised contrastive losses to encourage well-separated latent class representations. Experiments demonstrate that CORAL significantly improves both the diversity and visual quality of samples generated for tail classes relative to state-of-the-art methods.

Pause tokens, simple filler symbols such as "...", consistently improve Transformer performance on both language and mathematical tasks, yet their theoretical effect remains unexplained. We provide the first formal separation result, proving that adding pause tokens to constant-depth, logarithmic-width Transformers strictly increases their computational expressivity. With bounded-precision activations, Transformers without pause tokens compute only a strict subset of AC0 functions, while adding a polynomial number of pause tokens allows them to express the entire class. For logarithmic-precision Transformers, we show that adding pause tokens achieves expressivity equivalent to TC0, matching known upper bounds. Empirically, we demonstrate that two-layer causally masked Transformers can learn parity when supplied with pause tokens, a function that they appear unable to learn without them. Our results provide a rigorous theoretical explanation for prior empirical findings, clarify how pause tokens interact with width, depth, and numeric precision, and position them as a distinct mechanism, complementary to chain-of-thought prompting, for enhancing Transformer reasoning.

Unlike prior approaches constrained to fixed instrument classes, MGE-LDM learns a joint distribution over full mixtures, submixtures, and individual stems within a single compact latent diffusion model. At inference, MGE-LDM enables (1) complete mixture generation, (2) partial generation (i.e., source imputation), and (3) textconditioned extraction of arbitrary sources. By formulating both separation and imputation as conditional inpainting tasks in the latent space, our approach supports flexible, class-agnostic manipulation of arbitrary instrument sources. Notably, MGE-LDM can be trained jointly across heterogeneous multi-track datasets (e.g., Slakh2100, MUSDB18, MoisesDB) without relying on predefined instrument categories. Audio samples are available at our project page .

Open-World Object Detection (OWOD) enriches traditional object detectors by enabling continual discovery and integration of unknown objects via human guidance. However, existing OWOD approaches frequently suffer from semantic confusion between known and unknown classes, alongside catastrophic forgetting, leading to diminished unknown recall and degraded known-class accuracy. To overcome these challenges, we propose Combinatorial Open-World Detection (CROWD2), a unified framework reformulating unknown object discovery and adaptation as an interwoven combinatorial (set-based) data-discovery (CROWD-Discover) and representation learning (CROWD-Learn) task. CROWD-Discover strategically mines unknown instances by maximizing Submodular Conditional Gain (SCG) functions, selecting representative examples distinctly dissimilar from known objects. Subsequently, CROWD-Learn employs novel combinatorial objectives that jointly disentangle known and unknown representations while maintaining discriminative coherence among known classes, thus mitigating confusion and forgetting. Extensive evaluations on OWOD benchmarks illustrate that CROWD achieves improvements of 2.83% and 2.05% in known-class accuracy on M-OWODB and S-OWODB, respectively, and nearly 2.4 unknown recall compared to leading baselines. Figure 1: Overall Architecture of CROWD showing our novel combinatorial data-discovery guided representation learning approach to (a) identify unknown objects3 and (b) learn distinguishable representations of both known and unknown objects.

We present LMFusion, a framework for empowering pretrained text-only large language models (LLMs) with multimodal generative capabilities, enabling them to understand and generate both text and images in arbitrary sequences.

This paper introduces a novel kernel-based formulation of the Equalized Odds (EO) criterion, denoted as $\operatorname{EO}_k$, for fair representation learning (FRL) in supervised settings. The central goal of FRL is to mitigate discrimination regarding a sensitive attribute $S$ while preserving prediction accuracy for the target variable $Y$. Our proposed criterion enables a rigorous and interpretable quantification of three core fairness objectives: independence ($\widehat{Y} \perp S$), separation--also known as equalized odds ($\widehat{Y} \perp S \mid Y$), and calibration ($Y \perp S \mid \widehat{Y}$). Under both unbiased ($Y \perp S$) and biased ($Y \not \perp S$) conditions, we show that $\operatorname{EO}_k$ satisfies both independence and separation in the former, and uniquely preserves predictive accuracy while lower bounding independence and calibration in the latter, thereby offering a unified analytical characterization of the tradeoffs among these fairness criteria. We further define the empirical counterpart, $\widehat{\operatorname{EO}}_k$, a kernel-based statistic that can be computed in quadratic time, with linear-time approximations also available. A concentration inequality for $\widehat{\operatorname{EO}}_k$ is derived, providing performance guarantees and error bounds, which serve as practical certificates of fairness compliance. While our focus is on theoretical development, the results lay essential groundwork for principled and provably fair algorithmic design in future empirical studies.

Reasoning-trained language models often spend more tokens on harder problems, but longer chains of thought do not show whether a model is merely computing for more steps or following a different internal trajectory. We study this distinction through hidden-state trajectories during chain-of-thought generation across competitive programming, mathematics, and Boolean satisfiability. Raw trajectory geometry is strongly shaped by generation length: longer generations mechanically alter path statistics, so difficulty-dependent comparisons are misleading without adjustment. After residualizing trajectory statistics on length, difficulty remains systematically coupled to corrected trajectory geometry across all domains studied. The clearest reasoning-specific separation appears in the code domain, where harder problems show more direct corrected trajectories and less heterogeneous local curvature in reasoning-trained models than in matched instruction-tuned baselines. Corrected difficulty-geometry coupling is weaker, but still present, in mathematics and Boolean satisfiability. Prompt-stage linear probes do not mirror the code-domain separation, and behavioral annotations show that stronger corrected coupling co-occurs with strategy shifts and uncertainty monitoring. Together, these findings establish length correction as a prerequisite for generation-time trajectory analysis and show that reasoning training can be associated with distinct corrected trajectory geometry, with the strength of the effect depending on the domain.

Existing clustering methods for functional data often prioritize partitioning accuracy over interpretability, making it challenging to extract meaningful insights when the data-generating process follows a specific underlying structure and an ordinal relationship among clusters is suspected. This work introduces K-Models, a novel framework that integrates ordinal constraints and estimates key underlying elements of the random process generating the observed functional profiles, improving both interpretability and structure identification. The proposed method is evaluated through simulations and real-world applications. In particular, it is tested on Region of Interest (ROI) curves, which represent reaction profiles from a reflectometric sensor monitoring biomolecular interactions, such as antigen-antibody binding. These curves represent changes in reflected light intensity over time at multiple measurement spots with immobilized antigens during analyte exposure, capturing the binding dynamics of the system. The goal is to identify intrinsic signal patterns solely from the observed dynamics, making this dataset an ideal benchmark for assessing the added interpretability of the proposed approach. By incorporating structural assumptions into the clustering process, K-Models enhances interpretability while maintaining performance comparable to state-of-the-art techniques, providing a valuable tool for analyzing functional data with an underlying ordinal structure.

Most exploration algorithms search broadly until uncertainty is resolved. When the action space is too large to resolve within budget, practitioners default to $\varepsilon$-greedy, which bounds disruption but spends its override blindly. We introduce \textit{Delight-gated exploration} (DE), a host--override rule that spends exploratory actions only when their prospective delight (expected improvement times surprisal) exceeds a gate price. This practical heuristic recovers a classical result: Pandora's reservation-value rule for costly search, with surprisal setting the effective inspection cost. Resolved arms exit the gate, fresh arms shut off above a prior-determined threshold, and selected linear-bandit overrides consume finite information budget. Across Bernoulli bandits, linear bandits, and tabular MDPs, the same hyperparameters transfer without retuning, and DE shows much weaker regret growth than Thompson Sampling and $\varepsilon$-greedy in the tested unresolved regimes. Delight improves acting for the same reason it improves learning: it prices scarce resources by the product of upside and surprisal.